Trailing far behind is Edward R. Vrdolyak, the Republican candidate who switched from the Democratic Party in 1987. Black Control Since '83

A victory by the 46-year-old Mr. Daley, the State's Attorney of Cook County, would end six years of black control of City Hall. Harold Washington became the city's first black Mayor in 1983 by organizing a large and unified black turnout and also winning about 15 percent of the white vote. After Mr. Washington died in 1987, the City Council chose a black Alderman, Eugene Sawyer, as Acting Mayor. Mr. Daley defeated Mr. Sawyer in the Democratic primary in February.

The primary was one of the most racially divided elections here. Surveys of voters indicated only about 7 percent of them crossed racial lines when voting.

City election officials and polls say the voting population is roughly 40 percent white, 40 percent black and 7 percent Hispanic, with the balance Asian and others. Polls show that the Hispanic voters, while expected to turn out in relatively small numbers, heavily favor Mr. Daley.

Mr. Daley has raised more than $6 million for his campaign, the largest sum ever accumulated in such a short time by an Illinois politician. The money has bought a flurry of television and radio advertisments that cast him as a strong leader while largely avoiding discussion of his opponent.

Mr. Evans, 45, has criticized Mr. Daley as a captive of wealthy investors who wants to ''sell this city to some people in the suburbs.'' He has also accused Mr. Daley of planning to ''reopen his father's plantation,'' an allusion to the days of autocratic control of Mayor Richard J. Daley when blacks contended they were denied a fair share of city services and contracts. Mayor Daley died in 1976.

Last weekend, Mayor Daley's son told a predominantly white audience, ''People are tired of the bickering and the name-calling.'' He was referring to the racial antagonisms on the City Council that marked much of Mr. Washington's tenure and the contentiousness, mostly among black political factions, that followed his death. Denial of an Endorsement

Mr. Evans had sought the post of Acting Mayor, which Mr. Sawyer won largely on the strength of white support on the City Council. Mr. Evans, who launched his candidacy under the banner of the Harold Washington Party, refused to endorse Mr. Sawyer in the Democratic primary, which may have helped reduce black turnout. Mr. Evans has spent much of this campaign mending fences in the black community.

The Rev. Jesse Jackson, who lives here, has campaigned aggressively for Mr. Evans, as he had for Mr. Sawyer. He told supporters on the South Side today, ''Our family has come together.''

But Mr. Evans, who served as Mr. Washington's floor leader in the City Council, seems to have made little headway among white voters, polls indicate. Nor has Mr. Daley had much success among blacks, despite his frequent campaign visits to black churches and his promises to maintain hiring at City Hall at the ratio established by Mr. Washington.